For running in Asia and around China check out the Asia race calendar on the Shanghai running website. Shanghai running also host their own races in Shanghai, as do RunnersHai. AsiaTrailMaster also have foreigner registration for some big Chinese trail races. Be warned though, the big races in China like the Beijing and Shanghai marathons can only allow you to register for a short period of time and tend to close registration early, so you need to vigilant and keep checking the race website to be sure to get your number.